What is a bolt circle diameter (PCD)?

The pitch circle diameter (PCD), also called bolt circle diameter (BCD), is the diameter of the imaginary circle that passes through the centre of each bolt hole in a bolt pattern. For example, a 4x100 wheel bolt pattern means 4 bolts equally spaced on a 100 mm diameter circle. To find the PCD on an existing part, measure the distance between the centres of two adjacent bolts and divide by sin(pi/N), where N is the number of bolts.

How do I calculate the XY coordinates of bolt holes?

For bolt hole i (numbered from 0), the coordinates relative to the circle centre are: x = (PCD/2) x cos(start_angle + i x 360/N) and y = (PCD/2) x sin(start_angle + i x 360/N), where N is the total number of bolts and angles are measured in degrees. This calculator does the trigonometry for you and displays the coordinates for each hole.

What is the chord length between adjacent bolts?

The chord length is the straight-line distance between the centres of two adjacent bolt holes. The formula is: chord = PCD x sin(pi/N), where N is the number of bolts and pi is approximately 3.14159. For example, 6 bolts on a 100 mm PCD gives a chord of 100 x sin(30 degrees) = 50.00 mm. This measurement is useful for verifying bolt positions with a calliper without needing to locate the circle centre.

Bolt Circle Calculator

This calculator works out the exact geometry of a bolt circle - the ring of equally spaced holes found on wheels, flanges, couplings and drilling jigs, commonly described by its pitch circle diameter (PCD). Enter the pitch circle diameter in millimetres, choose the number of bolts from the preset list of 2 to 12 or select custom for any other count, then set a start angle measured in degrees anticlockwise from the 3 o'clock position and, if needed, an X and Y offset to shift the circle's centre away from the origin. The calculator instantly returns the bolt radius, the chord length between adjacent bolt centres, the angular spacing between holes, and the circumference of the full circle, along with a table listing the angle, X and Y coordinates and distance from origin for every bolt hole, plus a scaled diagram showing the pattern. Use it to lay out hole positions for a drilling jig or CNC program, to check a wheel or flange bolt pattern such as 4x100 or 5x114.3, or to work backwards and find an unknown PCD from a measured chord length. All coordinates are calculated using standard trigonometry to four decimal places. Because this is a planning tool, always confirm critical dimensions with a calibrated vernier calliper or other measuring equipment before drilling or machining, and round the results to the tolerance your job actually requires.

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Standard formula Coordinates use standard trigonometry: x = (PCD/2) × cos(θ), y = (PCD/2) × sin(θ).

1. Bolt Circle

Pitch circle diameter (PCD) mm

Number of bolts

Custom number of bolts

2. Options

Start angle degrees from 3 o'clock (positive X)

Coordinate origin offset X optional

Coordinate origin offset Y optional

Bolt Circle Results

Bolt Radius

PCD / 2

Chord Length
-
Adjacent bolt centre to centre

Angular Spacing

Degrees between bolts

Circumference

Arc length of full circle

Bolt Hole XY Coordinates

Bolt #	Angle (°)	X (mm)	Y (mm)	Distance from Origin (mm)

Bolt circle diagram (not to scale)

How Bolt Circle Calculations Work

A bolt circle (also called a bolt pattern or pitch circle) is a circular arrangement of equally spaced holes used in flanges, couplings, wheels, and machinery. Given the pitch circle diameter (PCD) and the number of bolts N, the key values are:

Radius (R): R = PCD / 2
Angular spacing: 360 / N degrees between each hole
Chord length: the straight-line distance between adjacent bolt centres = PCD × sin(π / N)
XY coordinates of bolt i (0-indexed): x = cx + R × cos(start + i × 360/N), y = cy + R × sin(start + i × 360/N)

Angles are measured in degrees from the positive X axis (3 o'clock direction), increasing anticlockwise. You can shift the start angle to place the first bolt at any position, for example 90 degrees to put the first bolt at the top (12 o'clock).

Worked Example

Defaults: 6 bolts on a 100 mm PCD, start angle 0 degrees, origin at (0, 0).

Radius = 100 / 2 = 50.00 mm
Angular spacing = 360 / 6 = 60.00 degrees
Chord length = 100 × sin(180 / 6) = 100 × sin(30°) = 100 × 0.5 = 50.00 mm
Bolt 1 (0°): X = 50.00, Y = 0.00
Bolt 2 (60°): X = 25.00, Y = 43.30
Bolt 3 (120°): X = -25.00, Y = 43.30
Bolt 4 (180°): X = -50.00, Y = 0.00
Bolt 5 (240°): X = -25.00, Y = -43.30
Bolt 6 (300°): X = 25.00, Y = -43.30

Common Bolt Patterns

Application	Pattern	Typical PCD	Chord Length
Car wheel (small)	4x100	100 mm	70.71 mm
Car wheel (large)	5x114.3	114.3 mm	67.19 mm
Car wheel (truck)	6x139.7	139.7 mm	69.85 mm
Industrial flange DN50	4x	125 mm	88.39 mm
Industrial flange DN100	8x	180 mm	68.88 mm

How to Measure PCD on an Existing Part

If you need to find the PCD of an existing bolt pattern, measure the distance between the centres of two adjacent bolt holes using a vernier calliper. Then use the formula: PCD = chord / sin(π / N). For example, if you measure 50 mm between adjacent holes on a 6-bolt pattern: PCD = 50 / sin(30°) = 50 / 0.5 = 100 mm. For a 4-bolt pattern, measure the centre-to-centre distance of two diagonally opposite bolts; that distance is equal to the PCD.

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Annulus Calculator: area and perimeter of a ring shape.

Method: Standard bolt circle trigonometry. Coordinates: x = cx + (PCD/2) × cos(θ), y = cy + (PCD/2) × sin(θ) where θ = start_angle + i × (360/N) in degrees. Chord length = PCD × sin(π/N). All values computed in double-precision floating point.

This calculator is for planning and reference purposes. Always verify dimensions with calibrated measuring equipment before machining or fabrication. Coordinate precision is to 4 decimal places; round to your required tolerance for workshop use.